Abstract:

The problem of high energy particles which cross a magnetohydrodynamic shock is difficult to analyse analytically. The reason is that the magnetic field has a kink over the shock and that it exists in the presence of an electric field. Thus far the only solutions for the problem are obtained numerically or approximately analytically. In this thesis the aim is to find an exact analytical expression for the acceleration of charged particles over such a magnetohydrodynamic shock. <br><br> Firstly, it is important to look at possible Lorentz transformations from the existing shock structure to a more simple structure in which the kink in the magnetic field disappears, or in which the electric field reduces to zero. In such a frame it is possible to find solutions of the equation of motion and to get an exact analytical expression for the energy gain of the particle over the shock. This expression depends only on the initial phase of the particle and another parameter which specifies the energy of the particle relative to the energy of the background plasma. <br><br> The obtained expression is evaluated in terms of results in the literature. It is shown that this expression reduces to the one obtained in the literature for the case of the magnetic moment being assumed constant. <br><br> It is important to know the energy gain for an isotropic particle distribution in the original shock structure. This is not so easy because the transformation results in an anisotropic distribution. Suggestions are given how to handle the anisotropy and an expression is written down for the averaged energy gain of an isotropic distribution. <br><br> Limitations of the present method and directions for future investigations are also discussed.